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If x^2  y^2 = 27, what is the value of (x + y)^2 ?
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02 Nov 2013, 00:47
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If x^2  y^2 = 27, what is the value of (x + y)^2 ? (1) y = 3 (2) x  y = 3 GH06.05.13  OE to follow
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Re: If x^2  y^2 = 27, what is the value of (x + y)^2 ?
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02 Nov 2013, 01:36
avohden wrote: If x^2  y^2 = 27, what is the value of (x + y)^2 ?
(1) y = 3
(2) x  y = 3
GH06.05.13  OE to follow From Stmt 1) y=3,then x^29=27=> x^2=36 =>x=6 or 6 then (x+y)^2 will be (6+3)^2=81 or (6+3)^2=9 Hence not sufficient From Stmt 2) (xy)=3 and x^2Y^2=27 =>(xy)(x+y)=27 =>(x+y)=9 =>(x+y)^2=81 Hence Stmt 2 alone is Sufficient Ans B



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If x^2  y^2 = 27, what is the value of (x + y)^2 ?
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Updated on: 02 Sep 2019, 07:24
avohden wrote: If x^2  y^2 = 27, what is the value of (x + y)^2 ?
(1) y = 3 (2) x  y = 3
Target question: What is the value of (x+y)²? Given: x²  y² = 27 Statement 1: y = 3 Take x²  y² = 27 and replace y with 3 to get: x²  (3)² = 27 Evaluate: x²  9 = 27 Simplify: x² = 36 So, EITHER x = 6 OR x = 6 Let's test each case: Case a: x = 6 and y = 3. So, (x + y)² = (6 + 3)² = 9² = 81. So, in this case, the answer to the target question is (x+y)² = 81Case b: x = 6 and y = 3. So, (x + y)² = (6 + 3)² = (3)² = 9. So, in this case, the answer to the target question is (x+y)² = 9Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: x  y = 3 Take x²  y² = 27 and FACTOR the left side to get: (x + y)(x  y) = 27 Replace (xy) with 3 to get: (x + y)(3) = 27 So, it must be the case that (x+y) = 9 If (x+y) = 9, then (x+y)² = 81 So, the answer to the target question is (x+y)² = 81Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B Cheers, Brent
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Originally posted by GMATPrepNow on 24 Jan 2018, 15:40.
Last edited by GMATPrepNow on 02 Sep 2019, 07:24, edited 1 time in total.



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Re: If x^2  y^2 = 27, what is the value of (x + y)^2 ?
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01 Sep 2019, 05:29
GMATPrepNow wrote: avohden wrote: If x^2  y^2 = 27, what is the value of (x + y)^2 ?
(1) y = 3 (2) x  y = 3
Target question: What is the value of (x+y)²? Given: x²  y² = 27 Statement 1: y = 3 Take x²  y² = 27 and replace y with 3 to get: x²  (3)² = 27 Evaluate: x²  9 = 27 Simplify: x² = 18 So, EITHER x = √18 OR x = √18 Let's test each case: Case a: x = √18 and y = 3. So, (x + y)² = (√18 + 3)². So, in this case, the answer to the target question is (√18 + 3)²Case b: x = √18 and y = 3. So, (x + y)² = (√18 + 3)². So, in this case, the answer to the target question is (√18 + 3)²NOTE: We need not actually calculate the values of (√18 + 3)² and (√18 + 3)². We need only see that the two values are DIFFERENT Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: x  y = 3 Take x²  y² = 27 and FACTOR the left side to get: (x + y)(x  y) = 27 Replace (xy) with 3 to get: (x + y)(3) = 27 So, it must be the case that (x+y) = 9 If (x+y) = 9, then (x+y)² = 81 So, the answer to the target question is 81Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B Cheers, Brent Posted from my mobile device



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Re: If x^2  y^2 = 27, what is the value of (x + y)^2 ?
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01 Sep 2019, 05:47
the solution is correct, however there is a calculation mistake where you subtract 9 from 27 rather than adding it.
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Re: If x^2  y^2 = 27, what is the value of (x + y)^2 ?
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05 Nov 2013, 22:42
Official Explanation
Answer: B  First, recognize that x^2  y^2 = (x + y)(x  y). That makes the expression a little more similar to what we're looking for  both this and (x + y)^2 contain a (x + y) term.
Statement (1) is insufficient. If y = 3, then x^2  9 = 27, so x^2 = 36. x must be either 6 or 6. If x = 6, the answer is (6 + 3)^2 = 81, but if x = 6, the answer is (6 + 3)^2 = 9.
Statement (2) is sufficient. Since (x + y)(x  y) = 27, if (x  y) = 3, then (x + y) = 9. We're looking for (x + y)^2, which is 9^2 = 81. Choice (B) is correct.



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Re: If x^2  y^2 = 27, what is the value of (x + y)^2 ?
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02 Dec 2017, 01:04
avohden wrote: If x^2  y^2 = 27, what is the value of (x + y)^2 ?
(1) y = 3
(2) x  y = 3
GH06.05.13  OE to follow x^2  y^2 = 27 OR (x+y)(xy) = 27 We need to find (x+y)^2, for which we need (x+y). Here various cases are possible for (x+y) and (xy).. Eg, former could be 9 and latter 3 or former could be 3 and latter 9 or former could be 3 and latter 9. (1) y=3. Substituting this we get x^2  3^2 = 27 OR x^2 = 27+9=36. Two values are possible for x here: 6 and 6, this will give two different answers for x+y. So Insufficient (2) xy=3. Substituting this we get (x+y)*3 = 27 or x+y =9. So we can get (x+y)^2. Sufficient. Hence B answer



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If x^2  y^2 = 27, what is the value of (x + y)^2 ?
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01 Sep 2019, 12:59
Analyzing the question:To figure out \((x + y)^2\) we only need \(x + y.\) Since we are given \(x^2  y^2 = (x  y)(x + y) = 27\), knowing \(x  y\) would also give \(x + y\) from that equation. Therefore we are trying to find \(x  y\), \(x + y\), or both values of x and y. Statement 1:(1) This gives us \(x^2 = 36\) but we don’t know if x is positive or negative. The two solutions give different values of \((x + y)^2\) so this is insufficient. Statement 2:(2) As stated above this is sufficient. Answer: B
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Re: If x^2  y^2 = 27, what is the value of (x + y)^2 ?
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02 Sep 2019, 07:24
ankitiofs wrote: the solution is correct, however there is a calculation mistake where you subtract 9 from 27 rather than adding it.
Posted from my mobile device Thanks for the heads up! I have edited my response accordingly. Cheers, Brent
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Re: If x^2  y^2 = 27, what is the value of (x + y)^2 ?
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